Daniel and Reggie have some money. If Daniel gives $119 to Reggie, the ratio of their money will be 3 : 5. If Daniel gives $623 to Reggie, the ratio of their money will be 1: 4. How much does Daniel have?
| |
Case 1 |
Case 2 |
| |
Daniel |
Reggie |
Daniel |
Reggie |
| Before |
15 u + $119 |
25 u - $119 |
8 u + $623 |
32 u - $623 |
| Change |
- $119 |
+ $119 |
- $623 |
+ $623 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Daniel has at first is the same in both cases.
15 u + 119 = 8 u + 623
15 u - 8 u = 623 - 119
7 u = 504
1 u = 504 ÷ 7 = 72
Amount that Daniel has
= 15 u + 119
= 15 x 72 + 119
= 1080 + 119
= $1199
Answer(s): $1199
